A New Mandatory-Optional Bipolar Model of Decision Making in a Fuzzy Environments

An extension of the basic Bellman and Zadeh’s [1] model of decision making in a fuzzy environment is discussed. The model in which the fuzzy environment is equated with fuzzy constraints on values of variables, fuzzy goals on values of performance functions, and a fuzzy decision which constitutes the aggregation of the fuzzy constraints and goals. The model provides a powerful conceptual and algorithmic basis for a multitude of decision making, optimization, control, etc. models. Traditional aggregation operators employed to combine the fuzzy constraints and fuzzy goals to form the fuzzy decision have originally been the minimum and than some other triangular norms, notably the algebraic product. In this paper, we propose to extend this aggregation to a nonstandard operator “and, if possible" which has been successfully employed in Zadrożny and Kacprzyk’s [19] approach to bipolar database queries. We present the basic, multivalued logic based approach to the processing of such “and, if possible” type aggregation in the context of the fuzzy model concerned.